Strathclyde Combinatorics Group
Department of
Mathematics and Statistics, University of Strathclyde
Research
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The main research
interests of the group lie in aspects of enumerative, bijective, algebraic
and topological combinatorics, with applications to computer science, physics
and biology. Much of our work has focussed on patterns in permutations and
other combinatorial objects. Central to this area is concept of a permutation
class, which is a downset under the permutation containment order. The study
of these structures began in the 1960s with Donald Knuth’s investigation of
computational sorting devices, which is still an active area of research.
Subsequently, they have been used to analyse models of genome rearrangement,
the layout of integrated circuits, and gas models in statistical physics,
among other things. |
Who are we?
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Sergey
Kitaev (Head of Group)
Sergey’s
research interests encompass aspects of enumerative and algebraic combinatorics,
combinatorics on words, and graph theory. Successes include the enumeration
of (2+2)-free posets via an encoding of them as ascent sequences. Sergey is
the author of two monographs, one on patterns in permutations and words, and
the other on words and graphs. Recently, he has pioneered the theory of
word-representable graphs (a topic on the boundary of graph theory and
combinatorics on words, with roots in algebra), including giving an effective
characterization in terms of graph orientations. |
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David Bevan
David’s
research interests mainly concern enumerative and asymptotic questions, particularly
in relation to permutations. Achievements include an explicit formula for the
growth rate of grid classes of permutations, and a structural
characterisation of the class of permutations avoiding 1324 together with new
bounds on its growth rate. Current research topics include the evolution of
the random permutation (as the number of its inversions increases),
permutation limits at different scales, and enumerative and structural
questions concerning permutation grid classes. |
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Elizabeth
Dombi
Elizabeth’s
research background lies in combinatorial semigroup theory, the algebraic
theory of formal languages, and combinatorial optimization concerning edge
covering of grid graphs. More recently, she has started working on
subdivision-resilience of non-word-representable graphs. |
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Einar
Steingrímsson
Einar’s
research interests primarily concern algebraic combinatorics, particularly in
relation to permutation patterns, and with an emphasis on permutation
statistics. He pioneered the concept of a vincular pattern, which has since
been generalised further by the notion of a mesh pattern. A particular focus
has been on the topology and Möbius function of intervals in the poset of
permutations ordered by pattern containment. Other recent work has concerned
the Abelian sandpile model, and the introduction and analysis of new
combinatorial structures whose motivation comes from particle physics. |
Research
visitor
• Herman Z.
Q. Chen, Chongqing Normal University (2024 – 2025)
Current PhD
students
• Humaira Hameed
(from 2023)
• Mohammed
Alshammari (from 2024)
• Nawaf Shafi Alshammari (from
2025)
Past events
• Scottish Combinatorics
Meeting 2023, 22–23 May 2023
• 
— Virtual Workshop,
15–16 June 2021
• 26th British
Combinatorial Conference, 3–7 July 2017
• Permutation Patterns 2012,
11–15 July 2012
• FPSAC 2011, 13–17
June 2011
Research
funding
• Shortening
universal words and DNA sequence assembly (Sergey Kitaev, Leverhulme
Research Fellowship, 2023–2024)
• Connecting
physics models via permutations (Einar Steingrímsson, Leverhulme Research
Fellowship, 2018–2020)
• New
combinatorial perspectives on the Abelian sandpile model (Mark Dukes and
Einar Steingrímsson, EPSRC, 2015–2018)
• The
Möbius function of the poset of permutations (Einar Steingrímsson, EPSRC, 2015–2018)
• Finding structure in sets of
permutations (Anders Claesson, Icelandic Research Fund, 2014–2016)
• Combinatorics of permutations and
words (Einar Steingrímsson, Anders Claesson, Sergey Kitaev and Mark Dukes,
Icelandic Research Fund, 2009–2012)
History
• The Strathclyde Combinatorics Group
had its origins in Gothenburg, Sweden, then moved to Reykjavík,
Iceland, before coming to Glasgow, Scotland. Einar has written a history of
the group, published in Enumerative Combinatorics and
Applications.
Former
faculty members of the group
• Anders Claesson (2011–2016; now Professor at the University of Iceland,
Reykjavík)
• Mark
Dukes (2011–2016; now Associate Professor at
University College, Dublin)
Former
research associates
• Thomas
Selig (2015–2018; now
Assistant Professor at Xi'an Jiaotong-Liverpool
University, Suzhou, China)
• Jason Smith (2015–2018; now
Senior Lecturer at Nottingham Trent University)
Former PhD
students
• Noura Alshammari (2021–2025): On the
asymptotic enumeration of monotone grid classes of permutations
• Dan Threlfall
(2020–2024; now Teaching Associate at the University of Strathclyde):
Thresholds for patterns in random compositions and random permutations
• Kittitat Iamthong (2018–2021; now Lecturer at Suranaree
University of Technology):
Encoding graphs by
words and morphisms
• Marc Glen (2016–2019): On word-representability of polyomino
triangulations and crown graphs
• Jason Smith (2012–2015; now
Senior Lecturer at Nottingham Trent University): On the Möbius
function and topology of the permutation poset
• Stuart Hannah (2011–2015): Interval order
enumeration